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Sunday, April 24, 2011

How Many Weeks are There in a Year?

What a question (you'd think)! Well, bear with me, because I have some news for you. I've previously blogged about the decline and fall of our higher education system, but there's always room for a little embellishment. One thing that I've learned over my years of teaching econometrics and economic statistics is that you should always expect the unexpected. It goes with the territory.

Here's a situation that I encountered a few years ago when I was teaching a first-level undergraduate economic statistics course. I recount it simply to illustrate the point that I learn something every time I step into the classroom, and certainly not out of disrespect for any particular individual(s). This is how it went down.
Picture if you will: I've just finished a lecture on how to seasonally adjustment economic time-series data, using the "ratio-to-moving-average" method, à la the (then) Census X-11 procedure. I'm feeling pretty chipper, because the class has obviously gone well and the students have clearly "got it". Time for a well-earned lunch. Alas, no! Coming towards me down the stairs of the 200-seater lecture hall is one really determined and annoyed looking dude. And he's he's definitely bigger than me! Elbowing his way through the happy throng at the front of the classroom, he puts his face in mine and demands, "What do you mean by saying there's 52 weeks in a year?" Being quick-witted I manage to blurt out "Cos there there are!", and that buys me a bit of time to reflect on my potential sins, and worry a little about what I could conceivably have said during the past 50 minutes that would have drawn this reaction.

Thinking back, I realize that about 20 minutes previously I was talking about the need to "center" the 4-quarter moving average, by taking a further 2-period moving average so as to re-align the data with the dates for the original time-series. I had casually remarked that with our calendar, this would always be necessary in practice. This is because we tend to measure "seasonal" economic data using seasons for which there is an even number each year: four quarters; twelve months; even 52 weeks. Without going into leap years, that's the nature of our calendar. That must have been it! I must have said something really dumb at that point (such as 50 weeks), while being distracted by some couple making out in the back row.

But no! A couple of other students, who are looking understandably bemused, assure me that I had said "52 weeks", and this simply motivates my upset customer to assert, "No there's not!" So back and forth we go for a couple of rounds: "Yes there are"; "No there's not"; and so on. The audience, which is growing in numbers by the round, stifles a few sniggers. Tiring of this delay to my hard-earned lunch, I strike a body-blow: "So, if there aren't 52 weeks in a year, how many are there?" I demand, feeling quite pleased with my tricky question. "48......... OF COURSE!" comes the response. "Everyone knows that!" (There's an implicit ".....stupid!" hanging in the air just waiting to fall at my feet.) So now we're back to more rounds of "No there's not"; "Yes there are"; and the other students are having a jolly old time!

This has to be brought to a conclusion, and quickly. The next class is starting to file into the room, and don't forget that he's bigger than me. I'm desperate! The verbal rounds are interspersed with vaguely insulting comments, apparently invoked by the sound of my (impossible-to-lose-at-my-age) New Zealand accent: "Well, in this part of the world there are 48 weeks!"; and "Is this some sort of foreign trickery?" This guy doesn't hesitate to hit below the belt.

Finally, I see him drop his guard for a second, and I'm in there like Muhammed Ali on a good day! "O.K.", I say. "Why exactly are there 48 weeks in a year?". My sparring partner looks puzzled, but recovers quickly, bless his heart. "Because everyone knows there are 12 months in a year, and there are 4 weeks in a month; and where I come from, 4 times 12 equals 48!" He looks triumphantly at his gathered class-mates, not noticing that most of them have their jaws firmly on the floor. (The implicit "stupid" is struggling to remain airborne.)

This calls for a knockout punch, so I manoeuvre into position and start my wind-up with the innocent question, "Well, how many days are there in a week?" Now he's eyeing me suspiciously - another bit of foreign trickery, perhaps? There's a pause as long as my much anticipated lunch-break, and then: "7?" That's all I need. "Right, so if there are 7 days in a week, and you say there are 4 weeks in a month, how many days are there in a month?" I receive a pitying look. "28 (of course!)", is the triumphant response. "Hmmm", I ponder aloud. "So what was the date yesterday?" A quick consultation of his day-planner yields the correct answer: "The 30th of September!", before he sags visibly and asks weakly, "Is this something new?"

I enjoyed my lunch that day, happy to have seen a ray of sunshine intrude into a dark corner of the campus.

In recent years most of my teaching has been graduate-level econometrics, but it wasn't always that way. For a couple of decades or more I taught elementary economic statistics at the first-year or second-year undergad. level, depending on where in the world I was at the time. It was a lot of fun. I can't imagine being in a job that's purely research and no teaching. The interactions and synergies are just too strong to resist, and interacting with students at an introductory level offers all sorts of special opportunities (for me) to learn new things.

Occasionally, students suggest to me that surely I must enjoy teaching grad. courses much more than introductory undergrad. ones. Not so, I always tell them. I enjoy teaching at different levels for different reasons. It's true - and not just because of memorable interactions such as the one I've described above! Students are then often quite puzzled when I go on to say that I've never taught an undergad. class without learning something new. That notion really conflicts with their prior, but again, it's true.

It's quite a tricky question though for students. I was sticking at my beliefs that actually in a month we got 4 weeks, so i just calculated with 12 to get calculation of how many weeks for a year and just realized when I saw your blog. Fyi, it helps my finance course so much, as I confused why in the hell the answer sheet said 52 weeks a year instead of 48.

Anonymous - Your point? We all know that the answer 364, and also that there are 365.25 days in a year - hence the leap years. No one is pretending that there are EXACTLY 52 weeks in a year. If you look at mortgage tables, etc, you'll see this "discrepancy" of 1.25 days is always taken into account.